Discrete Cosine Transform for 8x8 Blocks with CUDA Anton Obukhov
[email protected] Alexander Kharlamov
[email protected] October 2008 Document Change History Version Date Responsible Reason for Change 0.8 24.03.2008 Alexander Kharlamov Initial release 0.9 25.03.2008 Anton Obukhov Added algorithm-specific parts, fixed some issues 1.0 17.10.2008 Anton Obukhov Revised document structure October 2008 2 Abstract In this whitepaper the Discrete Cosine Transform (DCT) is discussed. The two-dimensional variation of the transform that operates on 8x8 blocks (DCT8x8) is widely used in image and video coding because it exhibits high signal decorrelation rates and can be easily implemented on the majority of contemporary computing architectures. The key feature of the DCT8x8 is that any pair of 8x8 blocks can be processed independently. This makes possible fully parallel implementation of DCT8x8 by definition. Most of CPU-based implementations of DCT8x8 are firmly adjusted for operating using fixed point arithmetic but still appear to be rather costly as soon as blocks are processed in the sequential order by the single ALU. Performing DCT8x8 computation on GPU using NVIDIA CUDA technology gives significant performance boost even compared to a modern CPU. The proposed approach is accompanied with the sample code “DCT8x8” in the NVIDIA CUDA SDK. October 2008 3 1. Introduction The Discrete Cosine Transform (DCT) is a Fourier-like transform, which was first proposed by Ahmed et al . (1974). While the Fourier Transform represents a signal as the mixture of sines and cosines, the Cosine Transform performs only the cosine-series expansion.